Statistics and Probability Answers

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In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is −0.38 ,

(a) An electrical firm manufactures fire balls that have a length of life that is approximately
normal distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find
the probability that a random sample of 16 balls will have an average life of less than 775
hours.
(b) The contents of seven similar containers of medicine are 9.8, 10.2, 10.4, 9.8, 10.0, 10.2 and
9.6 litres. Find a 95% confidence interval for the mean of all such containers, assuming an
approximate normal distribution
(c) In a random sample of 500 families owning an extingiusher sets in the city of Lusaka, Zambia,
it was found that 340 owned dry powder sets. Find a 95% confidence interval for the actual
proportion of families in this city with dry powder fire extinguisher sets.

If 99 people have a mean income of Birr 400, how much is the mean income increased by the addition of a
woman with an income of Birr 1500? A. Birr 412 B. Birr 410 C. Birr 411 D.Birr413

A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. We are interested in finding out if the average test scores are different for the different teaching methods.

If the original significance level for the ANOVA was 0.05, what should be the adjusted significance level for the pairwise tests to compare all pairs of means to each other?

A. 0.05
B. 0.25
C. 0.01
D. 0.5
E. 0.005

For given values of the sample mean and the sample standard deviation when n = 25, you conduct a hypothesis test and obtain a p-value of 0.0667, which leads to non-rejection of the null hypothesis. What will happen to the p-value if the sample size increases (and all else stays the same)?

A. Increase
B. Stay the same
C. Decrease
E. May either increase or decrease

A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.

Which of the following is the correct degrees of freedom for an F-test for evaluating if the average test scores are different for the different teaching methods?

A. dfG = 40, dfE = 4
B. dfG = 4, dfE = 40
C. dfG = 5, dfE = 45
D. dfG = 4, dfE = 44
E. dfG = 45, dfE = 4

We would like to test if students who are in the social sciences, natural sciences, arts \& humanities, and other fields spend the same amount of time studying for this course. What type of test should we use?

A. t-test for two independent groups
B. z-test
C. t-test for two dependent groups
D. F-test (ANOVA)

Which of the following is not a condition required for comparing means across multiple groups using ANOVA?

A. The observations should be independent within and across groups.
B. The variability across the groups should be about equal.
C. The data within each group should be nearly normal.
D. There should be at least 10 successes and 10 failures.

Air quality measurements were collected in a random sample of 25 country capitals in 2013, and then again in the same cities in 2014. We would like to use these data to compare average air quality between the two years. Which of the following tests is the most appropriate?

A. paired t-test with one-sided alternative hypothesis
B. independent samples t-test with two-sided alternative hypothesis
C. paired t-test with two-sided alternative hypothesis
D. independent samples t-test with one-sided alternative hypothesis

2. We are testing the following hypotheses:

H0: μ1 = μ2
HA: μ1 is not equal to μ2

The sample sizes are n1 = 20 and n2 = 40. Your friend who is working on this hypothesis test calculates a Z statistic, Z = 2.5. Which of the following is true?

A. She should be using an F statistic instead of a Z statistic.
B. p-value is approximately 0.006.
C. She should be using a T statistic instead of a Z statistic.
D. p-value is approximately 0.012.

1. An insurance company wants to estimate (using a confidence interval) its average claim amount using data from 20 randomly selected claims. Which of the following is false?

A. If the distribution of the sampled claim amounts is not extremely skewed, a T interval is appropriate.

B. The confidence interval can also be calculated using bootstrapping.

C. A confidence interval based on this sample is not accurate since the sample size is small.

D. The critical t-score, t* , has 19 degrees of freedom.

2. How does the shape of the t-distribution change as the sample size increases?

A. It becomes wider
B. It becomes more normal looking
C. It becomes flatter
D. It becomes skewed

Researchers studying IQ scores of 36 gifted children and their parents. First, differences in IQ scores were calculated as father's IQ score - mother's IQ score. The dot plot below shows the bootstrap distribution of means of 200 bootstrap samples taken from this original sample of differences in IQ scores. The mean of the bootstrap distribution is approximately -3.48 points and the bootstrap standard error is 1.3 points. Which of the following statements is false?

A. Since 0 is apparently an unusual value for the statistic, then at the 5% significance level we would fail to reject a null hypothesis of that claims that the fathers' and mothers' average IQs are equal.
B. A 95% bootstrap confidence interval for the difference in IQ scores is approximately (-6, -0.9).
C. It's likely that in the original sample, most mothers had higher IQ scores than the fathers.
D. A 90% bootstrap confidence interval for the difference in IQ scores would is approximately (-5.6, -1.3).